Invasive Plants: I have tons of dandilions in my yard!

and in my flower beds, I just pull those, or dig them and then I also use Preen and round up.
But I don't know what to do with the lawn, they are so thick.
If I put down some sort of grains, will they wash into my beds, or around my trees and kill those? I have lots of daylilies and iris mostly.
I just have so many, I am going to have to do something.

I didn't buy it from Amazon, although it does qualify for free shipping. I bought mine from Farm and Fleet. Not sure if you have that store, I know they're not everywhere.

If you use Round-Up, you can use a small box, cut out something similar to a mouse hole in the side of the box. Remove half of the top of the box. Holding the box (upside down, the cut off top on the ground) over the dandelion, gently spray Round-Up. I hope those directions make sense☺ Or, you can use a small painter's brush or foam brush, "painting" it on the dandelion. I use Round-Up for creeping charlie only. I mix the RU in a small spray bottle.

If you only have grass in your lawn, you can use 2-4D. It will kill the dandelions & not hurt the grass. If there are clovers, they will also die.
Trouble is the dandelions will keep coming from seed. Preen does not bother them at all. Preen is Treflan which is a grass killer.

To bad these garden centers & Wal Mart don't tell people what these chemicals really are.

Well I use preen in my beds and it certainly DOES prevent dandelions. It only prevents sprouting, it doesn't kill anything that is already growing, and preen does not kill any of the grass.
That said, I have a 1/2 acre lot and the dandelions are everywhere, there is no way I could treat them by hand or dig them.
I know they will continue to come up by seed. I know there are products I could put on the lawn that are safe for the grass. I am not worried about that, actually I have tons of clover and would love to be rid of that as well...

The trouble is I am not sure how to apply anything without hurting my plants in beds. When it rains will it wash into my beds and kill my plants?

Sounds like you've got the Preen pre-emergent. If you can find the Preen product in my second link that should work for you to kill existing weeds too (there are other brands that make similar products too if you can't find that one). Unless you live on a steep hill and get really bad runoff from the lawn into the garden beds the plants in your beds should be fine.

Weed Be Gon or 2-4D will only kill what it touches. So if you stay away from the good plants you will be OK. It won't spread around from rain. Spray on a calm day. It only kills broadleaf plants so it shouldn't bother lilies or Iris.
Personally, I will not spray my lawn. I have never sprayed or fertilized in the 28 years we have lived here. I mow at about 2½" & leave the clippings on the lawn. When they break down, they become fertilizer. Our lawn is healthy & doesn't have very many weeds. I do swab a thistle with Round Up no & then. Other weeds will disappear with regular mowing.
Flower beds are mulched with Cypress mulch. It lasts forever & don't use up the fertility of the soil like other woods do. An occasional dandelion gets pulled out.
This picture was taken yesterday.

I opened the links egrane3 provided & read the labels.
The first one is Garden Weed Preventor. It is Trifluralin, which is Treflan.
Dandelion is not on the list of weeds controlled.

The second is a lawn weed & feed product. It is 2-4D. 2-4D is normally sprayed as a liquid.
This is supposed to be applied dry, so I would wonder how it would work. 2-4D goes in through the plants leaves, so that is why it is sprayed to stay on the leaves.

I was a certified crop sprayer a number of years ago & used these products many times.
Bernie

If you're willing to go the chemical route, Scott's Super Turf Builder with Plus 2 weed control really works well - even if you have a whole lawn full of dandelions. It comes in granules so you can put it in a "spreader" with wheels or even a hand-crank spreader which makes it very easy to control. The only way the granules come is combined with a fertilizer, though, so you'd have to use it that way.

Supposedly Corn Gluten Meal works very well & it's a "natural" control, but it's a pre-emergent so you have to use it before you see the dandelions. It requires fairly large amounts and can be expensive in large quantities which is why we haven't tried it - we have a very large yard. If you have a 1/2 acre you'd have to decide whether you want to invest in it.

Bayer makes some very good products, including one for trees that actually kills the dreaded Emerald Ash Borer (which can save an Ash tree that would otherwise need to be cut down). They just came out with a whole line of supposedly natural products, though I haven't researched them so I can't vouch for them.